Operational amplifiers (opamps) are used in many different types of circuits including preamplifiers, variable gain amplifiers and the like. Referring now to FIG. 1A, an amplifier 20 includes an opamp 24 and a feedback path 28 that couples an output of the opamp 24 to an inverting input thereof. The non-inverting input is coupled to ground or another reference potential. The amplifier 20 in FIG. 1A has a gain value of one. For this reason, the amplifier 20 is usually called a unity-gain amplifier or buffer.
Referring now to FIG. 2A, an amplifier 30 is shown that is similar to the unity-gain amplifier 20 in FIG. 1A. However, in the amplifier 30, a resistance R is provided in the feedback path 28. Another resistance R is connected between an input of the amplifier 30 and the inverting input of the opamp 24. The amplifier 30 has a gain value of two.
The most relevant characteristics of an amplifier circuit are usually gain and bandwidth. In order to derive the bandwidth, an open loop response technique is used. The technique of looking at the open loop response provides information relating to the bandwidth and maximum achievable bandwidth of an amplifier circuit.
The DC gain of the open loop response is determined by opening the feedback loop and attaching a voltage source to an input side of the opened feedback loop. The output voltage is sensed at an output side of the opened feedback loop. Open loop response versions of the circuits in FIGS. 1A and 2A are shown in FIGS. 1B and 2B. To derive the bandwidth, the DC gain of the open loop response and the first dominant pole P1 are found. Assuming stable operation, there is only one dominant pole P1 located below the crossover frequency. The crossover frequency is the product of the DC gain of the open loop response and the first dominant pole P1. The crossover frequency usually defines the bandwidth of the closed-loop amplifier. The maximum available bandwidth is related to the second non-dominant pole P2.
Referring now to FIGS. 3A and 3B, the open loop response for the amplifiers in FIGS. 1B and 2B is shown, respectively. There is a constant gain from DC to a frequency of the first dominant pole P1. At the frequency of the pole P1, the gain begins falling. There is an inverse relationship between gain and bandwidth of the amplifiers 20 and 30. In FIG. 3A, the amplifier 20 has a gain of one. Therefore, the gain is constant until the zero crossing. In FIG. 3B, the gain is two until the intersection with the open loop response. In general, higher gain values are associated with lower bandwidth and lower gain values are associated with higher bandwidth. The bandwidth of the amplifier 30 is approximately half of the bandwidth of the unity-gain amplifier 20 while the gain of the amplifier 30 is twice the gain of the amplifier 20.
Referring now to FIG. 4, it may be desirable to adjust the frequency of poles P1 and P2 for some applications. For example, it may be desirable for the amplifier to provide a relatively constant bandwidth at different gain values. In FIG. 4, the gain values are relatively constant from DC up to the frequency of the first dominant pole P1. Because the first dominant pole P1 is close to the second non-dominant P2, the gain values fall off sharply upon reaching the first dominant pole P1.
Various compensation techniques are known for adjusting the frequency of the poles of the amplifier. The opamp may be implemented using a two-stage amplifier. In two-stage amplifiers, Miller compensation and Ahuja compensation are sometimes used. Miller compensation employs a feedback capacitor connected across an input and output of the second stage amplifier. In Ahuja compensation, a current gain device is added in the feedback loop of the second stage amplifier. Another compensation technique is used in folded cascode circuits that are output compensated. Specifically, a capacitor is coupled to an output of the circuit.
Referring now to FIGS. 3A, 3B and 5, it is difficult to adjust the frequencies of the poles P1 and P2 shown in FIGS. 3A and 3B without creating stability problems. In FIG. 5, the phase response that is associated with the open loop responses of FIGS. 3A and 3B is shown. The phase response is 180 degrees from DC to about the frequency of the first pole P1. At the frequency of pole P1, the phase response is approximately 90 degrees. The phase response remains at 90 degrees from the frequency of the first dominant pole P1 until about the frequency of the second non-dominant pole P2. At the frequency of the second non-dominant pole P2, the phase response is approximately zero degrees.
The phase response in FIG. 5 also illustrates a phase margin of approximately 90 degrees. The phase margin is usually defined at unity gain. For acceptable stability, the phase margin should be greater than approximately 55–60 degrees otherwise oscillation will occur. Therefore, the 90 degree phase margin that is shown in FIG. 5 is typically acceptable. However, moving the frequency of the second non-dominant pole P2 closer to the zero crossing will reduce the phase margin. At some point, this will cause oscillation. Conversely, moving the first dominant pole P1 closer to the zero crossing in FIGS. 3A and 3B will increase the phase margin. At some point, this too will cause oscillation. For these reasons, it is generally not possible to adjust the frequencies of the poles P1 and P2 shown in FIGS. 3A and 3B to produce the open loop response of FIG. 4 without creating stability problems.
Referring now to FIGS. 6A and 6B, a transimpedance amplifier (TIA) 60 includes an opamp 64 having a transconductance value (−gm). The opamp 64 has a feedback resistor (Rf) 66. A capacitance (C1) 70 is connected between an input of the TIA 60 and ground or a reference potential. Another capacitance (C2) 72 and a load resistance (RL) 74 are connected between the output of the TIA 60 and ground or a reference potential. An input 76 to the TIA 60 is a current I and an output 80 of the TIA 60 is a voltage V.
Referring now to FIG. 7, the open loop response for the TIA 60 in FIG. 6B is shown. At DC, the gain is equal to gmRL. If we assume that the capacitance C1 is much greater than the capacitance C2 and the resistance Rf is large, the frequency of the first dominant pole P1=1/(C1Rf). Further, the frequency of the second non-dominant pole P2=1/(C2*(RL in parallel with Rf)). The zero crossing occurs at a frequency of (gmRL)/(C1Rf).
Referring now to FIG. 8, the closed loop response for the TIA 60 is shown. Two different gain curves are illustrated in FIG. 8. One curve corresponds to the resistance Rf=Rf1 and the other curve corresponds to the resistance Rf=Rf2, where Rf2>Rf1. For a given value of Rf, higher gain is associated with lower bandwidth and lower gain is associated with higher bandwidth.